Low carbon economic dispatch for power systems with smoothed step carbon price functions

In the context of the "dual-carbon" target, carbon trading plays a crucial role in promoting energy efficiency and reducing emissions within the power system. Addressing the challenge of the existing low-carbon economic dispatch model's convergence issues and difficulty in achieving a global optimal solution, which stem from the discontinuous and non-smooth nature of traditional step-type carbon pricing functions, we propose a sigmoid-based step-carbon smoothing technique. This technique is employed to develop a multi-objective low-carbon economic dispatch model for the power system, encompassing carbon trading costs, electricity generation expenses, energy storage costs, and the percentage of renewable wind and solar energy curtailment. By smoothing the step-carbon pricing, we transform the multi-objective, fuzzy problem into a non-linear, single-objective optimization challenge. To solve this optimization problem, we utilize the sequential quadratic programming method, which is known for its strong convergence properties in mathematical terms. The findings indicate that, compared to the original segmented step function, the smoothing approach leads to further reductions in both carbon emissions and system costs.